Linear Algebra Done Right · Problem 5C.1

Eigenvalues, Eigenvectors, and Invariant Subspaces — Sheldon Axler

Mathematics — Linear Algebra · upper-triangular-matrices

Problem

Prove or give a counterexample: If

T \in \mathcal{L}(V)

and

T^2

has an upper-triangular matrix with respect to some basis of

V

, then

T

has an upper-triangular matrix with respect to some basis of

V